The number of the outcomes at two of the coins will turn up as head is 11
What is a combination?In mathematics, a combination or combinations are all the possible groupings that can be made of a given number of elements, without repeating them and regardless of the order in which they are found.
To solve this problem the formula and the combination procedure we must use is:
C(n/r) = n! / [(n-r)! *r!]
Where:
C(n/r) = combinationn = total number of objectsr = number of selected objects! = factorial of the numberInformation about the problem:
Number of outcomes in which 0 coins turns heads = 4C0Number of outcomes in which 1 coins turns heads = 4C1Number of outcomes in which 2 coins turns heads = 4C2Total number of outcomes = 4C0 + 4C1 + 4C2Applying the combination formula we have:
C(n/r) = n! / [(n-r)! *r!]
C(4/2) = 4! / [(4-2)! *2!]
C(4/2) = 4! / [(2)! *2!]
C(4/2) = 4*3*2! / [(2)! *2!]
C(4/2) = 4*3/2!
C(4/2) = 6
C(4/1) = 4! / [(4-1)! *1!]
C(4/1) = 4! / [(3)! *1!]
C(4/1) = 4*3! / [(3)! *1!]
C(4/1) = 4 / [1!]
C(4/1) = 4
C(4/0) = 4! / [(4-0)! *0!]
C(4/0) = 4! / [(4)! * 0!]
C(4/0) = 1
Total number of outcomes = 4C0 + 4C1 + 4C2
Total number of outcomes = 1 + 4 + 6
Total number of outcomes = 11
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16^x + 3 = 4^ (x+1)
solve for x with steps please
Modeling with Composite Functions
1. A store offers a 20% discount on all items and you also have a $3 coupon. Suppose you want to buy an item that originally costs $30.
a. Find the cost if applying 20% discount then $3 off.
b. Find the cost if applying $3 off then 20% discount.
c. Which should you apply first or does it matter?
Cost of the item in both cases are (a) $21 (b) $21.6 and (c) Lower price of the item is when applied 20% discount first and then $3 off.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Percentage is usually denoted by the symbol '%'.
(a) Original price of the item = $30
After 20% discount, price of the item = 30 - (30 × 20%)
= 30 - (30 × 0.2)
= $24
After $3 off, price of the item = $24 - $3 = $21
(b) Original price of the item = $30
After $3 off, price of the item = $30 - $3 = $27
After 20% discount, price of the item = 27 - (27 × 20%)
= $21.6
(c) The lower price is when applied 20% discount first and then $3 off.
Hence the price of the item is lower when we apply 20% discount first and then applied $3 off.
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Help please, i dont get this
Answer:
38°
Step-by-step explanation:
142° and x° are angles on a straight line. Angles on a straight line are equal to 180°
142° + x° = 180°
x° = 180° - 142°
x° = 38°
25. The wight to the nearest (kg) of a group of 50 people under a special diet are given below. Use the information to: (i) prepare a grouped frequency table using Sturges formula (ii) compute mean, mode and media. [17.5 marks] 65, 70, 60,46, 51, 55, 59, 63, 68, 53 47, 53, 72, 53, 67, 63, 64, 70, 57, 56 73, 56, 48, 51, 53, 72, 65, 62, 49, 64 53, 59, 63, 50, 43, 62, 67, 56, 61, 64 66, 52, 49, 62, 71, 58, 69, 53, 63, 59
Frequency table is provided in image and mean=57.28, mode=63 and meadian=61.5.
What is a frequency table ?
A frequency table consists of the lists of items in a given data set and the number of times each item occurs in the data set and The number of times a particular data value occurs in a given data set is referred to as its frequency.
e.g.
A, A, A, B, B, B, B, C, C, D
Count the number of times each grade occurs in the above series. Yes, ‘A’ occurs thrice, ‘B+’ occurs four times, ‘C’ occurs twice, and ‘D’ occurs once. Now, according to the definition of frequency, we can note the frequency of each grade as follows:
Frequency of A = 3
Frequency of B = 4
Frequency of C = 2
Frequency of D = 1
Let us list the grades obtained by the students in the above example, in a frequency table. Table is in image.
Now,
For given frequency table
Mean=sum of all values/no. of terms=2864/50=57.28
Mode=63 as the frequency is highest for 63
Median=(25th+26th) terms/2=61.5.
Hence,
mean=57.28, mode=63 and meadian=61.5.
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Please help me with this
Extra points s
Answer: It's D
Step-by-step explanation:
Find the volume of a right circular cone
that has a height of 19 ft and a base with a
diameter of 18.7 ft. Round your
answer to
the nearest tenth of a cubic foot.
Answer:
V = 31,667.8 cubic ft
Step-by-step explanation:
The volume of a right circular cone can be calculated using the formula:
V = (π * r^2 * h) / 3
Where r is the radius of the base and h is the height of the cone.
First, let's find the radius:
r = diameter / 2 = 18.7 ft / 2 = 9.35 ft
Now, we can plug in the values for r and h into the formula:
V = (π * 9.35^2 * 19) / 3 = (π * 87.5295 * 19) / 3 = (1670.20355 * 19) / 3 = 31,667.76 cubic ft
Rounding to the nearest tenth of a cubic foot, we get:
V = 31,667.8 cubic ft
1. A car costs $10,520 and decreases in value by 15% every year. How much will the car be worth after 4 years?
Answer:
5491.50575
Step-by-step explanation:
10520 x (1 - 0.15)^4
so first you subtract 1 from 0.15 and that equals 0.85 then you times 0.85 itself cuz it decreases value for a total of four years and that would make 0.85^4 =0.52200625 now you 10520 x 0.52200625= 5491.50575
ps. depending if your adding or subtracting percents it will either 1+ or 1- then whatever percent into decimal hope this helps!
Santiago's family took a road trip to Mount Rushmore. Santiago fell asleep 44% of the way through the trip. If the total length of the trip was 400 miles, how many miles had they travelled when Santiago fell asleep
Answer:
176 miles
Step-by-step explanation:
Step 1: determine what 44% of 400 miles is
44% of 400= 176
Answer: Santiago fell asleep at 176 miles and they had 224 miles left in their trip.
someone please helppp T^T
geometry : find the value of x
Answer:
x = 7
Step-by-step explanation:
In a triangle(3 sides), the total number of degrees is 180 degrees.
In a quadrilateral(4 sides), the total number of degrees is 360 degrees.
^^ Now convert this into a formula
Let's say s = number of sides
d = total degrees
s: d:
3 --> 180
4 --> 360
Hence, the relation between s and d is:
(s-2)*180
Let's test this relation:
3:
(3-2)*180 = ==> plugin 3 for s in (s-2)*180
1*180 = 180 √
4:
(4-2)*180 = ==> plugin 4 for s in (s-2)*180
2*180 = 360 √
Now apply this formula to an 8-sided figure:
s = 8
(s-2)*180 =
(8-2)*180 = ==> plugin 8 for s in (s-2)*180
6*180 = 1080 total degrees in the 8-sided figure
Since all 8 sides in the 8-sided figure are equal, all 8 angles are equal as well.
Hence, the measure of each angle is:
1080 / 8 = 135 degrees
Hence:
16x + 23 = 135 ==> solve for x
16x = 112 ==> subtract 23 on both sides to isolate x
x = 7 ==> divide both sides by 16 to isolate x
what is the area under the normal distribution that is between the mean and one standard deviation away from the mean?
About 68% of the area is covered by one standard deviation above and below the mean, therefore one standard deviation above the mean corresponds to 34% of the area. Thus, we have 84% after adding the 50% below the mean and the 34% above the mean.
A normality assumption with a zero mean and a standard error of one is referred to as the typical normally distributed. The standard normal distribution is centered at zero, and the standard deviation indicates how much a specific measurement deviates from the mean.
Sixty-eight percent of the observations for the normal distribution are within one standard deviation of the mean, ninety-five percent are within two standard deviations of the mean, and ninety-nine percent are within three standard deviations of the mean.
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Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
The equations for price of one tire patch
4x + 1.9 = 22.2
22.2 – 4x = 1.9
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
We have to find the Equation for price of one tire patch.
Ryan bought 4 tire patches.
Price on gift card= $22.2
Then, according situation the equations for price of one tire patch
4x + 1.9 = 22.2
and, 22.2 – 4x = 1.9
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he Georgia Aquarium broke the record for the world’s largest aquarium in 2005 with a tank that holds 6.3 million gallons of water. How many of these record-breaking tanks would it take to house the same one billion goldfish (that are each 3 inches long)? Round your answer to the nearest tank.
Which of the following numbers is NOT divisible by 8?
A. 1,406
B. 1,488
C. 3,608
D. 5,016
Answer:
[A] 1406
Step-by-step explanation:
To see which is NOT divisible by 8 all we have to do is divide each answer choice by 8.
Not divisible means that the answer is a whole number (Not a decimal).
[A] 1406/8 = 175.75
[B] 1488/8 = 186
[C] 3608/8 = 451
[D] 5016/8 = 627
As we can see, the only one that is not divisible by 8 is [A] 1406.
RevyBreeze
What is the answer in a percentage?
The monthly interest rate for the principal is 0.64%
How to determine the monthly rate?Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.
The formula for compound interest is
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
Since the annual interest rate (r) is 7.7%. The monthly interest rate can be calculated by dividing the annual interest rate by 12 (There are 12 months in a year).
Thus, monthly interest rate = 7.7 / 12 = 0.64%
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The perimeter of a square must be greater than 182 inches but less than 198 inches. Find the range of possible side lengths that satisfy these conditions. (Hint: The perimeter of a square is given by P=4s, where s represents the length of a side).
Express your answer in interval notation. Use decimal form for numerical values.
The range of possible side lengths that satisfy these conditions is,
⇒ { s | 45.5 < s < 49.5 }
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
The perimeter of a square must be greater than 182 inches but less than 198 inches.
Now, We know that;
The perimeter of a square is given by,
⇒ P = 4s
Where, 's' represents the length of a side.
Here, The perimeter of a square must be greater than 182 inches but less than 198 inches.
Hence, We get;
⇒ 182 < P < 198
Since, P = 4s
⇒ 182 < 4s < 198
⇒ 182/4 < 4s/4 < 198/4
⇒ 45.5 < s < 49.5
Thus, The range of possible side lengths that satisfy these conditions is,
⇒ { s | 45.5 < s < 49.5 }
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One solution contains 2 parts salt to 8 parts water, and another contains 3 parts salt 5 parts water. How much of each should be mixed together in order to obtain 280 quarts of a solution that is 3 parts salt to 7 parts water? Please help very urgent!
In a case whereby one solution contains 2 parts salt to 8 parts water, and another contains 3 parts salt 5 parts water. the number of each part that should be mixed together in order to obtain 280 quarts of a solution that is 3 parts salt to 7 parts water are: x = 160 quarts and 120 quarts respectively.
How can the number of each part that should be mixed be calculated?The concept that will be used here is simplification
The salt concentration can be expressed by turning them to decimal form and these area;
Solution A: [2/(2 + 8)]
= [2/10]
= 0.20 salt
We can as well expresss the Solution B in term of fraction as:
: [3/(3 + 5) ]
= [3/8 ]
= 0.375 salt
We can as well express the Mixed Solution in term of fraction we can be done as
:[ s/(3 + 7)]
= 3/10
= 0.30 salt
The mixture is said to be 280 quarts, however in the case whereby 0.375 salt can found in the mixed solution that is denoted as " x" , we can know the 0.20 salt, which can be expressed as [y = 280 – x]
Then we can compute the typical mixture equation as :
[0.375x + 0.20(280-x)] = [0.30(280)]
If we simplify we have
[0.375x + 56 - 0.20x] = 84
It can be simplied further as
[0.375x - 0.20x + 56 – 56] = [84 – 56]
Then after the summation from the left sides we have
[0.375x - 0.20x] = 28
[0.175x ]= 28
Then, we can find the value of x as
x= 28/0.175
x = 160
Since the value of x is known we can find the value of Y as :
y = [280 – x]
y = [280 – 160]
Then the value of y can be expressed as :
y = 120
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To produce each product unit, the company spends $1.75 on material and $2.95 on labor. Its total fixed cost is $6000. Each unit sells for $6.35.
What is the smallest number of units that must be sold for the company to realize a profit?
The smallest number of units that must be sold for the company to realize a profit will be 3,637 units.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
To produce each product unit, the company spends $1.75 on material and $2.95 on labor. Its total fixed cost is $6000. Each unit sells for $6.35.
Let 'x' be the number of units. Then the equation is given as,
6.35x = 1.75x + 2.95x + 6000
Simplify the equation, then we have
6.35x = 1.75x + 2.95x + 6000
6.35x = 4.7x + 6000
1.65x = 6000
x = 3637 units
The smallest number of units that must be sold for the company to realize a profit will be 3,637 units.
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Triangle LMN is formed by connecting the midpoints of the side of triangle IJK. The measures of the interior angles of triangle IJK are shown. Find the measure of
Please need help with5,6,and7
According to the exterior angle theorem, the exterior angle that results from stretching a triangle's side is equal to the sum of the dimensions of the triangle's two opposed interior angles.
What is theorem of exterior angles?According to the exterior angle theorem, the exterior angle that results from stretching a triangle side is equal to the sum of the dimensions of the triangle's two opposed interior angles. Three internal angles in a triangle or polygon always add up to 180 degrees. This theorem is applied to each of the outer angles, which total six.
Here,
Given :
With the help of the triangle's well-known features, we can validate the exterior angle theorem.
Think about an ABC.
The total of the three angles is 180 degrees (angle sum property of a triangle) ——- Equation 1: (A+B)/180 ——- Example 2 (rewriting equation 1)
e = 180 - c
——- Equivalent 3 (linear pair of angles)
Equation 3 may be solved for by substituting the value of c.
e = 180 - [180 - (a + b)]
e = 180 - 180 + (a + b)
e = a + b.
=> m∠A = m∠G
=> m∠DMG > m∠A
So , its proven that:
=> m∠DMG > m∠G
and
=> A-D-M
So,
AD = DM
=> AD <AM
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Helpp me please guysssssssssssssssssss
Answer:
y = 4 and lh = 16
Step-by-step explanation:
hi again
A rectangular floor of area 28.8 m2 is going to be tiled. Each tile is rectangular, and has an area of 400 cm2. An exact number of tiles can be put into the space. How many tiles will be needed?
Answer:
(28800 cm2) / (400 cm2/tile) = 72 tiles
Step-by-step explanation:
A volume is described as follows:
1. the base is the region bounded by y=6−3/8 x^2 and y=0
2. every cross-section parallel to the x-axis is a triangle whose height and base are equal.
Find the volume of this object.
volume =
A volume is described as follows:
1. the base is the region bounded by y=e^1.9x, y=1.9x^2+0.5, and x=1;
2. every cross-section perpendicular to the x-axis is a square.
Find the volume of this object.
volume =
The volume of the solid generated will be 201 cubic units
Let's rotate it around the y-axis rather than x = 0.
(x-5)² = 4 - y → y = 4 - (x - 3)²
The parabolic section's area is A.
= 2 · int_0^2 (4 - x²) dx = 2(4x - x^3/3)|_0^2 = 32/3
At x, there is a horizontal centroid.
x = 3, so C = 2π(3) = 6π
V = A · C = 32/3 · 6π = 64π cubic units.
Cylinder method: V = 2π int_1^5 (4x - x(x-3)²)) dx = 2π int_1^5(-x^3 +6x² - 5x) dx
V = 2π(-x^4/4 + 2x^3 - 5x²/2)|_1^5 = 2π[(-625/4 + 250 -125/2) - (-¼ + 2 - 5/2)]
V = 2π(125/4 + 3/4) = 2π(32) = 64π cubic units
About 201 cubic units.
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The question would be:
What is the volume of the solid generated when the region bounded by the curve (x-5) ^2 =4-y and the x-axis is revolved around the line x=2?
the students in a first-grade class were all asked to time how long (in seconds) they could hold their breath. the results were tallied and are presented in the following histogram. how many of those students held their breath greater than 12.5 but less than 15.5 seconds?
Based on the histogram, 13 students held their breath for greater than 12.5 seconds but less than 15.5 seconds.
In a first-grade class, students measured how long they could hold their breath. The results were shown on a graph called a histogram. To see how many students held their breath between 12.5 and 15.5 seconds, we need to look at the bars on the graph between those times. The number of students is shown by the height of each bar.
We can see that there are 2 students who held their breath between 12.5 and 13.5 seconds. There are 5 students who held their breath between 13.5 and 14.5 seconds. And there are 6 students who held their breath between 14.5 and 15.5 seconds. To find out the total number of students, we add the heights of the bars together.
So:
2 + 5 + 6 = 13Hence, there are 13 students who held their breath between 12.5 and 15.5 seconds.
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A high school basketball coach wants to see whether there is a linear relationship between player height, x, and the number of points scored in a game by basketball players in the coach's state, y. The 96 percent confidence interval to estimate the slope of the linear regression line relating player height to points scored in a game is calculated to be ( -.0.432, 1.844 ).
Assume all conditions for inference for the slope of a regression line were met. Based on the confidence interval, which of the following claims is supported by the confidence interval?
Choose matching definition
O We are 95 percent confident that the mean increase in the weight of a black bear for each one-year increase in the age of the bear is between 7.0 and 18.4 pounds.
O We are 96 percent confident that the average increase in mating call frequency in the population of frogs when habitat temperature increases by 1 degree Celsius is between 1.573 and 3.109 tones per second.
O It cannot be determined whether the linear relationship between player height and number of points scored for basketball players in the coach's state is positive or negative.
O We can be 95% confident that wind speed decreases, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.
The answer is C. There is a positive linear relationship between player height and number of points scored for basketball players in the coach's state.
A confidence interval is a range of values that is calculated from the data and is believed to contain the true population parameter with a certain level of confidence, in this case 96%. The slope of the regression line is the average change in y for a one unit change in x, which represents the direction and strength of the relationship between x and y.
The confidence interval for the slope is (−0.432,1.844), which does not include 0, which means that the slope is not equal to 0. If the slope were 0, there would be no relationship between player height and points scored. The fact that the confidence interval is positive means that the slope is positive, which indicates a positive linear relationship between player height and number of points scored.
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Place a single word into each sentence to make it correct, then place each sentence into a logical paragraph order describing haemostasis Coagulation aggregate
inhibits
Thrombopoiesis
vascular
promotes
Drag the text blocks below into their correct order. ____ finishes the process by clotting the blood and protecting the body from excess blood loss.
In platelet plug formation, a large mass of platelets ___ and undergo degranulation three First, ___ Spasm constricts the broken blood vessel, reducing haemorrhage.
Degranulation ____ haemostasis There are ___ mechanisms haemostatic
Hemostasis is the process that causes a blood vessel to stop bleeding. It is a multi-step process with connected steps.
Here are the right answers in the right sequence.
Hemostatic mechanisms come in THREE varieties.
First, a VASULAR spasm tightens the blood vessel that has ruptured, limiting bleeding.
A significant amount of platelets AGGREGATE and go through degranulation during the creation of platelet plugs.
DEGRANULATION AIDS IN HEMASTASIS
Blood turns from a liquid to a gel during COAGULATION, also known as clotting, creating a blood clot. Hemostasis, the stoppage of blood loss from a damaged vessel, and repair may be the outcomes. The activation, adhesion, and aggregation of platelets, as well as the deposition and maturation of fibrin, are all components of the coagulation process.
After an injury, coagulation starts virtually right after.
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find the volumes of the solids generated by revolving the regions about the given axes. If you think it would be better to use washers in any given instance, feel free to do so. The region bounded by y = 2x - x^2 and y = x about the line x=1
The volume of the solid generated by revolving the region bounded by y = 2x - x^2 and y = x about the line x=1 can be found using the method of cylindrical shells. The method involves slicing the solid into thin cylindrical shells, finding the volume of each shell, and then summing the volumes of all the shells to find the total volume of the solid.
We start by finding the equations for the two curves:
y = 2x - x^2,
y = x
We then find the points of intersection between the two curves:
2x - x^2 = x
x^2 - x - 2 = 0
x = 2 or x = -1
Since the solid is generated about the line x=1, we only consider the part of the region that lies to the right of x=1, which corresponds to x=2. The radius of each cylindrical shell is equal to the difference between the x-coordinate of the upper curve and x=1, which is 1. The height of each shell is equal to the difference between the y-coordinates of the two curves at x=2, which is (2x - x^2) - x = 2 - 4 = -2.
The volume of cylindrical shell is:
V = πr^2h
Plugging in the values:
V = π * (1^2) * (-2)
V = -2π
The total volume of the solid is the sum of the volumes of all the cylindrical shells, which is just -2π. The volume is negative because the height of each shell is negative, which indicates that the solid is being generated in the opposite direction.
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coaching and sat scores what we really want to know is whether coached students improve more than uncoached students, and whether any advan- tage is large enough to be worth paying for. use the information above to answer these questions: (a) how much more do coached students gain on the aver- age? construct and interpret a 99% confidence interval.
With 99% confidence that the true difference lies between 0.1316 and 0.2694.
A 99% confidence interval for the difference in average SAT scores between coached and uncoached students can be constructed using the data above.
The confidence interval is calculated as (mean of coached students - mean of uncoached students) +/- (2 * standard error of the difference in means).
The mean of coached students is (0.3098 + 0.3399 + 0.219 + 0.0798) / 4 = 0.2155, and the mean of uncoached students is (0.0046 + 0.0248) / 2 = 0.0147. The standard error of the difference in means can be calculated as the square root of ((0.2155(1-0.2155)/4) + (0.0147(1-0.0147)/2)).
The confidence interval is then (0.2155 - 0.0147) +/- (2 * 0.0347) = 0.201 +/- 0.0694, or (0.1316, 0.2694). This indicates that, on average, coached students gain 0.201 points more than uncoached students, with 99% confidence that the true difference lies between 0.1316 and 0.2694.
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Task 1 gifts & entertainment 12% clothes 5% misc. 7% $144.38 savings 10% $52.94 debt 5% Spending of net incomes) Guidelines housing 30% food 20% transportation 11% Janice has a monthly net income of $3,850. Based on this amount and the percentages in the Spending Guidelines to the left, how much should she spend in the following categories? 1: rent 1: How much can Janice spend on rent? 3: savings 2: monthly bus pass for work 4: student loan payment 2: How much can Janice spend on a monthly bus pass for work?
When taking out a loan, the borrower must provide collateral such as a car or home to reduce the risk to the lender and increase the chances of the loan being approved. This includes rent, monthly bus pass, savings, student loan payment, and other expenses.
What do you mean by loan?A loan is a type of debt that is typically provided by a financial institution such as a bank, credit union, or finance company. The purpose of a loan is to provide the borrower with a large sum of money that they may not have readily available, which they must then pay back over a set period of time with interest.
There are various types of loans, including personal loans, car loans, home loans, and student loans. Personal loans are unsecured loans that can be used for a variety of purposes, such as debt consolidation or home improvement. Car loans are used specifically to purchase a vehicle, while home loans are used to purchase a home. Student loans are designed to help pay for education expenses.
When taking out a loan, the borrower is typically required to provide some form of collateral, such as a car or a home, to secure the loan. This helps to reduce the risk to the lender and increases the chances of the loan being approved.
1. Rent: 30% of $3,850 = $1,155.
2. Monthly bus pass for work: 11% of $3,850 = $423.
3. Savings: 10% of $3,850 = $385.
4. Student loan payment: 5% of $3,850 = $192.5.
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Solve the following system of equations graphically on the set of axes below.
y= 2x-1
y= -3x-6
I NEED TO KNOW HOW TO GRAPH ITTTT!!!!
By graph, the solution of the system of equations is (- 1, - 3).
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
The system of equations are,
⇒ y - 2x - 1
⇒ y = - 3x - 6
Now, We can draw the graph of given system of equations.
The red line shows the graph of y = 2x - 1 and blue line shows the graph of y = - 3x - 6.
So, By graph;
Both equations are cut into at point (- 1 , - 3).
Hence, By graph, the solution of the system of equations is (- 1, - 3).
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An individual is presented with three different glasses of cola, labeled C, D, and P. He is asked to taste all three and then list them in order of preference. Suppose the same cola has actually been put into all three glasses. What are the simple events in this ranking experiment? (Enter your answers as a comma-separated list.What probability would you assign to each one?A. It is impossible to determine the probability of the simple events with the given information.B. The probability of an individual event where D is ranked first is 1/12. The probability of another individual event is1/4.C. The probability of an individual event where D is ranked first is 1/5.The probability of another individual event is 1/15.D. All of the simple events have the same probability, 1/6.E. All of the simple events have the same probability, 1/3.
The simple events in this ranking experiment are C-D-P, C-P-D, D-C-P, D-P-C, P-C-D, P-D-C where all of the simple events have the same probability, 1/6.
The simple events in this ranking experiment are the 6 possible ways the individual can order the three glasses of cola: C-D-P, C-P-D, D-C-P, D-P-C, P-C-D, P-D-C.
Since the individual's preferences are assumed to be random and the same cola has been put into all three glasses labeled C, D, and P, each of the 6 possible ways the individual can order the glasses (C-D-P, C-P-D, D-C-P, D-P-C, P-C-D, P-D-C) are equally likely.
This means that each of the 6 simple events has a probability of 1/6, or 0.1667. This is because if each ordering of the glasses is considered an outcome, there are 6 equally likely outcomes. The probability of any one of the outcomes is 1 divided by the total number of outcomes, or 1/6.
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